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Question 4: A company medical director failed to find significant evidence that the mean blood pressure of a population of executives differed from the national mean μ = 128. The medical director now wonders if the test used would detect an important difference if one were present. For a random sample of size 72 from a normal population of executive blood pressures with standard deviation σ = 15, the z statistic is
√
z = (x ̄ − 128)/(15/ 72)
The two-sided test rejects
H0 :μ=128 at the 5% level of significance when |z| ≥ 1.96.
(a) . Find the power of the test against the alternative μ = 135.
(b) . Find the power of the test against μ = 121. Can the test
be relied on to detect a mean that differs from 128 by 7?
(c) (1 mark). If the alternative were farther from H0, say μ = 138, would the power be higher or lower than the values calculated in (a) and (b)?
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